How to use a constraint to make a roller paint animation?
You can make the stick movement control the rotation of the roller:

Create your object, parent the roller to the stick:



Give your roller a Transformation constraint with this kind of setup: Stick as Target, Extrapolation on, Target and Owner &gt; Local Space, Map From &gt; Location with the stick local movement orientation as axis (choose for example -1 and 1 as value, anyway it will be extrapolated), Map To &gt; Rotation with the roller rotation movement axis as destination axis, don't forget to select the target location axis as Source (and choose the rotation value that will match):


Move the stick, the roller should rotate according to the stick speed: